The moments of coverage of a linear set
Irwin Greenberg · Journal of Applied Probability · 1980
A number of points are chosen at random along a line segment and used as the left end-points of lengths of fixed size. Finite sum expressions are derived for the moments of the portion of the line segment covered by one or more of the lengths. The derivation utilizes a relationship between the coverage and the busy time in an M / D /∞ queue.